Number
system
•
Natural
numbers:Denoted
by
N
=
{1,23,4,......
Number
system
•
Whole
numbers:Denoted
by
W=
{0,1,2,3,4,....)
•
Integers:Denoted
by
Z
or
|={...2,-1,0,1,2,...
Note:
(Positive
integers)={1,2,3,4,.=Natural
numbers
(Negative
integers)-1,-2,-3,-4,...
(Non-negative
numbers
integers)={0,1,2,3,4,.}=Whole
(Non-positive
integers)={0,-1,-2,-3,-4,.}
•
Even
numbers:Integers
which
are
divisible
by
2
are
called
even
numbers.
example:..6,4,-2,0,2,4,6,8,.}
•
Odd
numbers:lntegers
which
are not
divisible
by
2
are
called
odd
numbers.
example:{...3,-1,1,3,5,7,....
•
Prime
numbers:Natural
numbers
which
are
divisible
by
1
and
itself
only.
example:2,3,5,7,11,13,17,19,23...
•
Composite
numbers:Let
'a'
be
a
natural
number,
'a'
is
said
to
be
composite
if,it
has
atleast
three
distinct
factors.
example:{4,6,8,9,1
0,12,14,15,16,18,20,22,.
Note:
Composite
numbers
=Non
prime
numbers
Every
prime
number
z5
ccan
be
of
form
6k+1,where
'k'
is
natural
number.
example:
5=6*1-1
(6k+1)
13=6*2+1
•
Rational
numbers:
Numbers
which
can
be
expressed
in
'p/a'
form,where
p
and
q are
integers
such
that
q0.Rational
numbers
are
denoted
by
Q.
example:2/3,7/1,-5/7...
Every
integer
is
rational
number
but
every
rational
number
is
not
integers.
•
Irrational
numbers:
Numbers
which
can
not
be
expressed
in
p/q
form.
example:
-/2,\4,L,etc.
•
Co-prime
numbers:
Two
natural
numbers(not
necessarily
prime)
are
called
co-prime
,if
their
H.C.F.(Highest
common
factor)
is
one.These
numbers
are
also
called
relatively
prime
numbers.
example:(9,25)(6,25)(2,5)(8,9)(99,100)etc.
•
Twin
prime
numbers:lf
the
difference
between
two
prime
numbers
is
two,then
the
numbers
are
called
twin
prime
numbers.
example:(3,5)(17,19) (29,31)(11,13)etc.
Created
with
Mi
Notes
